Question

which angles are consecutive interior angles?

image of lines and angles with points h, e, k, i, f, p, j, g

options:
∠efi and ∠hif
∠gfd and ∠jif
∠gfd and ∠hik
∠jik and ∠efi

Explanation:

Step1: Recall Consecutive Interior Angles Definition

Consecutive interior angles are two angles that lie between two lines (the "interior") and on the same side of a transversal. The two lines are cut by the transversal, and the angles are consecutive (adjacent in terms of the transversal's position) between the two lines.

Step2: Analyze Each Option

• Option 1: $\angle EFI$ and $\angle HIF$

Let's identify the lines: The two lines here seem to be $HE$ (or $HJ$) and $EG$ (or $FG$), with transversal $KP$ (the line through $I$ and $F$). $\angle EFI$ is between the two lines (inside the region bounded by $HJ$ and $FG$) and on one side of the transversal, and $\angle HIF$ is also between the two lines and on the same side of the transversal. Let's check the other options to confirm.

• Option 2: $\angle GFD$ and $\angle JIF$

$\angle GFD$ is outside the region between the two main lines (closer to $G$), while $\angle JIF$ is inside. They don't lie between the same two lines, so not consecutive interior angles.

• Option 3: $\angle GFD$ and $\angle HIK$

$\angle GFD$ is near $G$, $\angle HIK$ is at $I$ on the other side of the transversal. Not between the same two lines.

• Option 4: $\angle JIK$ and $\angle EFI$

$\angle JIK$ is at $I$ on the outer side, $\angle EFI$ is inside. Not between the same two lines.

Answer:

$\angle EFI$ and $\angle HIF$ (the first option)